C a r s h o p! WebQuest Instructions Introduction: Within the next year or two you will probably have a driver s license. One thing leads to another and sooner or later it will be time to buy a car. What can algebra do to prepare you for this exciting event? Let s go car shopping and find out! Task: You will be granted a loan for your first car woohoo! if you can convince the loan officer that you are not a poor financial risk. To prove that you are financially wise beyond your years you must study two payment options, choose the smartest one, and explain your reasoning. If you do not succeed, your loan will be denied, so judge carefully. Process Day 1: Choose one or two partners, go shopping, investigate the relationships between variables. Dream Away! It s not real, so go shopping first and worry about financing later. 1. Forget about a budget be realistic if you want to be, or go for your ultimate dream car at http://www.cars.com/go/index.jsp. Happy hunting! In the New Cars section of the Buy window select Make & Model; enter zip code. Click on Find a New Car. Assume that you will be paying MSRP: manufacturers suggested retail price. Use the tabs to Select Style, Add Color, Add Options, & See Vehicle Summary. Print the Summary. 2. Investigate the variables that influence how you will pay for your car at http://www.lendingtree.com/common/bp/autotrader4/autohowmuchcalc.asp?bp=autotrader4&esourceid=397860&source=397860#. Play with the dials on the dashboard until you ve figured out how each of the variables affects the others. Jot down some notes below. Later, you ll use what you learn to convince the loan officer that you are financially savvy for one so young. Notes These variables influence the size of my monthly payment: Examples (give several): When the interest rate increases then These variables influence how much I can borrow (loan amount): Examples (give several): When term length decreases then
Process Day 2: Create two payment plans, complete a loan application. Show Me the Money! You ve found the car; now you ve got to find the money. 3. Using the auto loan calculator at this link develop two different payment plans for the car you have selected: http://www.lendingtree.com/stmrc/java/autoloan.asp?bp=autotrader4 When the first plan is complete use the file menu to print. In page range, choose to print only one page. Also print the second plan when finished. Besides price of the car, the variable that you will control is the down payment (cash down). To make the math more interesting, choose a plan with a large down payment and a plan with little or no down payment. Set the term (number of months to pay back the loan) at 60 for both plans. Also set the interest rate 8% and tax rate 6.5% for both plans. Assume that you have no trade-in. Use the default non-taxable fee of $40. Before you leave the site check out all three graphs in the purple section of the loan calculator and take some notes. Notes: How does the term length affect monthly payment? How does the down payment affect monthly payment? The down payment for my first payment plan is The monthly payment for my first payment plan is The down payment for my second payment plan is The monthly payment for my second payment plan is 4. Now that you have a couple of plans it s time to get started on the paperwork. Fill out but DO NOT SUBMIT a loan application at this site. Print a copy of the application. https://www.capitaloneautofinance.com/loan/applynow/loanapp.aspx?pffsrcid=adcc10hp*autbtm*tl0206*** If you are short on time print a blank application. Fill it out by hand at home tonight.
Process Day 3: Apply what you know about lines to the car shopping experience. Use Your Noggin! It s time to organize and analyze the data you ve collected. 5. Write a slope-intercept equation for each of your two payment plans. Equation for plan #1 Equation for plan #2 6. Use a graphing calculator to create a table and graph that compare the plans. If you do not have a graphing calculator, go to http://www.coolmath.com/graphit/index.html 7. Use the calculator to find the point of intersection of the two lines. 8. Using the y-intercepts and the point of intersection to guide you, transfer your graph to graph paper. (This will go on a poster; make it large.) 9. Transfer your table to paper or to a spreadsheet and print. (This will go on a poster; make it large.) Hint: set your calculator table to record total paid in six month increments. 10. Prepare to visit the loan officer by thinking about the data you have collected. Some questions to consider are: What variables influence how you will pay for the car? How do these variables affect each other? What does each equation mean? X represents Y represents The slope is it represents The y-intercept is it represents Where does each of the pieces you just listed appear in the table and the graph? What is the solution to the system of equations? Does it have any significance in this problem? Why or why not? Why are the y values for each plan different at 60 months even though both plans buy the same car at the same price? Which of the two payment plans have you chosen? Why?
Process Day 4: Communicate effectively about your learning. Be on Your Best Behavior! It s time to visit the loan officer. The moment of truth has arrived. The loan officer will evaluate your financial and mathematical knowledge to decide whether or not to approve you for a loan. Make sure your data is well-presented and be prepared to explain your thinking. Make a poster that you will use to present the two financing options to the loan officer. This will help explain why one plan is better, and convince her that you are a safe risk for her company. You will also share this poster with the class. The poster will include the summary sheet about your car (with photo), the graph, table, equations, and both payment plans. It will specify which plan you chose and say why. Depending on her schedule the officer may or may not ask you about everything you have prepared. Bring along this form with your notes and written answers to questions so if she has a busy day she can read your responses at her leisure. At the discretion of the loan officer you may be asked to share parts of your presentation with the class. At a minimum you will be required to display your poster. Notes: on main points I will make to impress the loan officer with my financial wisdom: Here s how I will use my poster to communicate my main points effectively:.
Extension 1: Take this challenge if you finish early Remember using the red dashboard dials to investigate the relationship between variables? Go back to your day one notes and use the clues below to find four examples of direct variation and two examples of inverse variation. Direct Variation: as one variable increases so does the other variable. 1. 2. 3. 4. Inverse Variation: as one variable increases the other decreases. 1. 2. Think of real-world variables outside this project that are related. Give at least one example of two variables that have a direct relationship. Give at least one example of two variables that have an inverse relationship. Extension 2: What can a ruler teach you about paying for a car? Plan with less cash down a. Length of segment from 0 to 60 months: b. Length of segment from month 0 to month where total price of car (including taxes and fees) is paid: c. Segment a minus b: Hint: Use a metric ruler Plan with more cash down d. Length of segment from 0 to 60 months: e. Length of segment from month 0 to month where total price of car (including taxes and fees) is paid: f. Segment d minus e: Why is b longer than e? Why is c longer than f? Compare c/b to f/e. What did you find and what does it mean?